A right circular cone of base radius R, height H, and known density ps floats base down in a liquid of unknown density pf. A height h of the cone is above the liquid surface. Derive a formula for pf is terms of ps, R, and h/H, simplifying it algebraically to the greatest possible extent. [Recall Archimedes' principle, stated in the preceding problem, and note that the volume of a cone equals (base area) (height)/3.]